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A sufficient condition for dominating cycles

✍ Scribed by J.A Bondy; Genghua Fan


Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
214 KB
Volume
67
Category
Article
ISSN
0012-365X

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Two sufficient conditions for dominating
✍ Mei Lu; Huiqing Liu; Feng Tian πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 148 KB

## Abstract A cycle __C__ of a graph __G__ is dominating if each component of $G\backslash C$ is edgeless. In the paper, we will give two sufficient conditions for each longest cycle of a 3‐connected graph to be a dominating cycle. Β© 2005 Wiley Periodicals, Inc. J Graph Theory

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Nous prouvons une conjecture due & Bondy et Fan. Un cycle C d'un graphe G est dit m-dominant si tout sommet de V(G -C) est a distance au plus m de C. Notre r&t&at est: si G est k-connexe, et si G n'a pas de cycle m-dominant, alors il existe un stable de cardinal k + 1, dont les sommets sont deux 3 d

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## Abstract Let __G__ be a 2‐connected graph of order __n.__ We show that if for each pair of nonadjacent vertices __x__,__y__ ∈ __V(G)__, then __G__ is Hamiltonian.